The Spaniard is scheduled to have more talks with owner Dave Whelan about his future as the relegated club try to hang on to their in-demand manager.
Martinez has been linked with the Everton vacancy but asked Whelan last week for certain commitments in regards to developing the training ground and youth system.
The chairman has been mulling over the implications, both financial and otherwise, and an outcome is expected later.
"Everyone wants to be here next year and obviously the gaffer is at the head of everything we do here," Caldwell told the Wigan Evening Post.
"A lot of other clubs will be wanting to take him and rightly so.
"But obviously we all want him to stay here and help us to get back into the Premier League as quickly as possible.
"It's his decision, and it will be a big decision to make.
"Whatever he decides we'll wish him well, but on behalf of the players here we're desperate for him to stay."
- Sports & Recreation
- Dave Whelan